From OrangeCar Stuff:
A hexacube is a 3 dimensional object obtained by joining 6 (unit) cubes at a face of each of the 6 cubes in such a way that neighboring cubes have a full face in common and any cube has at least one neighbor. HexacubeX is an application that allows you to view and manipulate the 166 different hexacubes. The 166 hexacubes can be arranged in a 10x10x10 cube with 4 empty spaces (6 x 166 = 996). One way to do this is described at http://www.bumblebeagle.org/polycubes/hexacubes/solution.html The hexacube displayed at the right is shown as it is oriented in that solution. Above it are the coordinates within the 10x10x10 box at which it is located in a coordinate system that has its Y axis pointing to the right, its Z axis up and its X axis right-hand perpendicular (coming out of the screen toward you). Below it is its offset from (0, 0, 0) and the the orientation relative to +X, +Y and +Z. The hexacube on the left is the same as the one on the right but oriented according to the right hand slider setting. The right hand slider controls which of the 24 possible orientations is shown. Above it are the coordinates it would have if placed at the origin of the coordinate system with that orientation. Below it is the coordinate system rotation designation resulting from its displayed orientation. The hexacubes are numbered as described in the article HEXACUBES by Jean Meeus and P.J.Torbin in the Journal of Recreational Mathematics volume 30, number 2 (1999-2000). In addition to using the sliders to change the hexacube displayed and its orientation you can use the steppers or enter their numbers in the associated text boxes and pressing return or enter.
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